3.3.3 Counting with Bijections Video
PROFESSOR: An elementary idea that gets you a long way in counting things is this idea of counting with bijections, which is counting one thing by counting another. And we can illustrate that by example. Let's begin with looking at some stuff that is easy to count using just the simple sum and product rules. So suppose that I'm trying to count passwords. This is a contrived, over-simplified example, but it gives you the idea. And this is what I mean by a password. A password is a sequence of characters that are either letters or digits subject to the constraints that they are supposed to be between six and eight characters long. They're supposed to start with a letter, and they're case sensitive. So you can tell the difference between uppercase and lowercase letters. So let's define the set L of all the letters-- uppercase and lowercase together. And let D be the set of digits from 0 through 9. Then we said that passwords are supposed to be between six...